Surface coating for reduction of aerodynamic noise and vibrations

ABSTRACT

A coating apparatus for the reduction of aerodynamic noise and vibrations. The coating apparatus is configured to include a group of fibrillar structures, wherein each fibrillar structure is configured with a diverging tip so that the coating reduces the size of and shifts downstream, a separation bubble, and modulates large-scale recirculating motion. Each fibrillar structure can be configured as a cylindrical micropillar. The group of fibrillar structures can be configured as a group of uniformly distributed cylindrical micropillars (e.g., one or more micropillar arrays). The surface coating is effective in reducing the separation bubble and displacing the separation bubble downstream. The coating facilitates a reduction in noise (e.g., aerodynamic noise) and vibrations due to the reduction in the size of the separation bubble.

STATEMENT OF GOVERNMENT RIGHTS

The invention described in this patent application was made withGovernment support under Contract Number NSF/ONR CBET-1512393 awarded bythe Office of Naval Research and the National Science Foundation. TheGovernment has certain rights in the invention.

TECHNICAL FIELD

Embodiments are related to the field of flow separation in fluidmechanics and devices, systems and techniques for reducing flowseparation. Embodiments also relate to surface coatings for reducing theamount of drag produced in turbulent flow. Embodiments further relate tosurface coatings that facilitate the reduction of aerodynamic noise andvibrations.

BACKGROUND

Flow separation is a fluid mechanic phenomenon that results in increaseddrag and loading on structures, causing reduced energy efficiency andpossibly compromising structural integrity. As an object travels througha fluid, the velocity of the fluid in contact with the object slows downbecause of the viscosity of the fluid and the friction applied by theobject's surface. This interaction between the fluid and the surface ofthe object is referred to as the boundary layer, which can becategorized as either laminar or turbulent flow by calculating theReynolds number (i.e., a ratio of inertial force to viscous force). LowReynolds numbers are attributed to larger viscous forces, which resultin laminar flow (e.g., constant, orderly fluid motion). As the Reynoldsnumber increases because of large inertial forces, the flow becomesdisorderly (e.g., producing eddies and vortices) and transitions intoturbulent flow.

With respect to aerodynamics, the boundary layer profile begins aslaminar and transitions to turbulent as the velocity profilethickens—disrupting the smooth flow and producing skin-friction drag. Atgreater downstream distances of an object traveling through a fluid, theboundary layer and the pressure differential (e.g., front-to-back ofobject) increase—eventually resulting in a separation bubble thatreverses the flow at the surface. When the flow reverses, the boundarylayer essentially separates from the surface, creating a drag force thatrequires more energy to overcome and in some cases causes a plane tostall.

In addition to turbulent flow, an object's surface roughness hasdemonstrated an ability to increase the skin-friction drag andpotentially play a role in flow separation. To overcome this issue,researchers have been investigating the use of coating on surfaces toreduce the amount of drag produced in turbulent flow.

BRIEF SUMMARY

The following summary is provided to facilitate an understanding of someof the innovative features unique to the disclosed embodiments and isnot intended to be a full description. A full appreciation of thevarious aspects of the embodiments disclosed herein can be gained bytaking the entire specification, claims, drawings, and abstract as awhole.

It is therefore one aspect of the disclosed embodiments to provide formethods and devices for reducing flow separation.

It is another aspect of the disclosed embodiments to provide for methodsand devices that reduce the amount of drag produced in a turbulent flow.

It is yet another aspect of the disclosed embodiments to provide for asurface coating for the reduction of noise and vibrations due to areduction in the size of a separation bubble.

It is also an aspect of the disclosed embodiments to provide for amicro-scale fibrillar coating that reduces flow separation by reducingthe size of a separation bubble and pushing the separation point furtherdownstream.

The aforementioned aspects and other objectives and advantages can nowbe achieved as described herein. A surface coating is disclosed for thereduction of aerodynamic noise and vibrations. In an example embodiment,a coating apparatus can be configured, which includes a group offibrillar structures, wherein each fibrillar structure is configuredwith a diverging tip so that the coating reduces the size of and shiftsdownstream, a separation bubble, and modulates large-scale recirculatingmotion. In some example embodiments, each fibrillar structure can beconfigured as a cylindrical micropillar. Such a group of fibrillarstructures can be configured as a group of uniformly distributedcylindrical micropillars.

The coating is configured to function under dry or wet conditions andmitigates flow separation without a noticeable increase in theproduction of TKE (Turblent Kinetic Energy). The coating can beconfigured as a microsurface coating that shifts the separation pointdownstream and reduces the area of negative flow. The coating can alsobe configured to rely on the generation of distributed wall-normalperturbations.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, in which like reference numerals refer toidentical or functionally-similar elements throughout the separate viewsand which are incorporated in and form a part of the specification,further illustrate the disclosed embodiments and, together with thedetailed description of the disclosed embodiments, serve to explain theprinciples of the present invention.

FIG. 1 illustrates a pictorial diagram depicting a sample shark denticleand sample microscopy images of micropillar arrays, in accordance withan example embodiment;

FIG. 2 illustrates graphs depicting data indicative of instantaneousnormalized velocity for respective smooth and coated cases, and graphsof data indicative of the mean vertical velocity for the smooth andcoated cases, respectively, in accordance with an example embodiment;

FIG. 3 illustrates a graph depicting superimposed contour lines for thenormalized mean streamwise velocity and graphs with data indicative ofvelocity profiles, in accordance with an example embodiment;

FIG. 4 illustrates graphs depicting profile data and a schematic diagramdemonstrating the physical mechanism by which a group of micropillarsmodify the flow in the area near the flow, in accordance with an exampleembodiment;

FIG. 5 illustrates a schematic diagram of the APG test section of awind-turbine, in accordance with an example embodiment;

FIG. 6 illustrates a schematic diagram depicting a ZPG test section andFIG. 6A illustrates an inset thereof, in accordance with an exampleembodiment; and

FIG. 7 illustrates a flow chart of operations depicting a method forfiber fabrication in accordance with an example embodiment.

DETAILED DESCRIPTION

The particular values and configurations discussed in these non-limitingexamples can be varied and are cited merely to illustrate at least oneembodiment and are not intended to limit the scope thereof.

The embodiments will now be described more fully hereinafter withreference to the accompanying drawings, in which illustrativeembodiments of the invention are shown. The embodiments disclosed hereincan be embodied in many different forms and should not be construed aslimited to the embodiments set forth herein; rather, these embodimentsare provided so that this disclosure will be thorough and complete, andwill fully convey the scope of the invention to those skilled in theart. Like numbers refer to identical, like or similar elementsthroughout, although such numbers may be referenced in the context ofdifferent embodiments. As used herein, the term “and/or” includes anyand all combinations of one or more of the associated listed items.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an”, and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this invention belongs. It will befurther understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Subject matter will now be described more fully hereinafter withreference to the accompanying drawings, which form a part hereof, andwhich show, by way of illustration, specific example embodiments.Subject matter may, however, be embodied in a variety of different formsand, therefore, covered or claimed subject matter is intended to beconstrued as not being limited to any example embodiments set forthherein; example embodiments are provided merely to be illustrative.Likewise, a reasonably broad scope for claimed or covered subject matteris intended. Among other things, for example, subject matter may beembodied as methods, devices, components, or systems. The followingdetailed description is, therefore, not intended to be taken in alimiting sense.

Throughout the specification and claims, terms may have nuanced meaningssuggested or implied in context beyond an explicitly stated meaning.Likewise, the phrase “in one embodiment” or “an example embodiment” asused herein does not necessarily refer to the same embodiment and thephrase “in another embodiment” as used herein does not necessarily referto a different embodiment. It is intended, for example, that claimedsubject matter include combinations of example embodiments in whole orin part.

In general, terminology may be understood at least in part from usage incontext. For example, terms, such as “and”, “or”, or “and/or,” as usedherein may include a variety of meanings that may depend at least inpart upon the context in which such terms are used. Typically, “or” ifused to associate a list, such as A, B or C, is intended to mean A, B,and C, here used in the inclusive sense, as well as A, B or C, here usedin the exclusive sense. In addition, the term “one or more” as usedherein, depending at least in part upon context, may be used to describeany feature, structure, or characteristic in a singular sense or may beused to describe combinations of features, structures or characteristicsin a plural sense. Similarly, terms, such as “a,” “an,” or “the,” again,may be understood to convey a singular usage or to convey a pluralusage, depending at least in part upon context. In addition, the term“based on” may be understood as not necessarily intended to convey anexclusive set of factors and may, instead, allow for existence ofadditional factors not necessarily expressly described, again, dependingat least in part on context.

During the past few decades, considerable effort has been placed oncontrolling flow separation. This phenomenon is usually responsible forincreased vibration and drag on bluff bodies as well as higher energyconsumption in vehicles. The drag experienced by a body under subsonicmotion mostly embodies viscous and pressure (form) effects. The formeris a result of friction induced by the near-wall fluid, and the latteris a result of pressure imbalance around the surface of the body. Theseparation phenomenon is well exemplified in the canonic case of flowaround a foil at a sufficiently high angle of attack. There, the adversepressure gradient (APG) in the suction side leads to flow decelerationand eventually flow detachment. The direct consequence of this processis a change of the aerodynamic force components, namely lift and drag.

Surface roughness plays a significant role in the turbulence dynamicsnear the wall and, in particular, in the separation regions. Evidencesuggests that randomly distributed roughness, e.g., sand grainroughness, may move the separation point against the flow direction inthe case of foils; this shift results in drag increase and liftdecrease. Experiments have shown an upstream shift of the separationpoint in a channel expansion with rough walls. However, various studieshave shown that triggering transition to turbulence may reduceseparation. These findings have motivated the use of flow controlstrategies such as vortex generators and synthetic jets to effectivelydelay flow separation. Unfortunately, these methods increase theproduction of TKE (Turbulent Kinetic Energy), which, in turn, increasesviscous losses and thus energy dissipation near the wall region. Thisviscous loss suggests that the control of flow separation withoutturbulence penalty is an ideal way to control form drag.

Recent efforts have focused on passive control via bio-inspiredsurfaces. The morphology of some natural organisms such as the lotusleaf and shark skin suggests that this daunting task might be achievedthrough textured coatings. Synthetic microscale structures similar tothose found in the lotus leaf have been effective in reducing viscousdrag by creating a slip velocity with trapped air between the wall andthe water flow. The surface, however, eventually wets, losingfunctionality over tim. Denticles found on the skin of sharks have alsoshown drag reducing properties. While not completely understood, thesestructures appear to inhibit the formation and evolution of near-wallcoherent motions. However, the physical mechanism responsible for thisphenomenon is still under debate.

FIG. 1 illustrates a pictorial diagram depicting a sample shark denticle10 and sample microscopy images 14 and 16 of micropillar arrays, inaccordance with an example embodiment. The example shark denticle 10shown in FIG. 1 demonstrates a divergent shape with an asymmetry in thewall-normal and streamwise directions. The example microscopy images 14and 16 of such micropillar arrays have a similar asymmetric shape (e.g.,note—scale bars: 100 μm). Note that in the example images 14 and 16, theheight and tip diameter of each element are 85 μm and 75 μm, whereas thesalk diameter is 40 μm. The center-to-center distance between thepillars is 120 μm. Note that throughout the specification, exampleparameters such as those depicted in the figures and described herein,should not be considered limiting features of the disclosed embodimentsbut are discussed and illustrated for exemplary purposes only.

A feature of shark denticles as illustrated in FIG. 1 is theaforementioned asymmetric geometry. The pillars shown in images 14 and16, for example, are axisymmetric but take other elements of thedenticles, including divergence and height. They are packed in aCartesian layout and feature a “spatula” shape with stalk and tipdiameters of 40 μm and 75 μm, respectively, a height of 85 μm (definedhere as the roughness height, k), and a center-to-center distancebetween pillars of 120 μm. Another key difference is that the pillars donot include the channel-like indentations that denticles have on theirtop surfaces. Note that the pillars shown in the images 14 and 16 can bearranged in a square packing with aligned rows and columns, butnaturally occurring denticles overlap and are randomly aligned.Synthetic denticles have been successfully tested in Cartesian arrayswithout overlap. One of the objectives of the disclosed embodiments isto demonstrate that this unique, engineered microsurface is capable ofmitigating flow separation. The pillars' simple manufacturing andcost-effective fabrication process may lead to a large impact in a widerange of energy applications.

Despite some success fabricating shark-inspired synthetic surfaces, suchfabrication methods rely on 3D printing, making it difficult toreplicate denticles in their original size. Some experiments have scaledthe structures by a factor of 12.4 to satisfactorily replicate geometricfeatures. However, because every denticle must be 3D printed, thismethod may be slow and expensive. The approach described and presentedherein instead relies on a series of etching and casting steps. Whilethe initial step includes a complicated process composed of deepreactive ion etching, the subsequent steps allow for replication of thedesired surface using simple casting methods. Once a mold is made, itcan be used almost indefinitely. This reusability allows forreproduction and scaleup of these engineered microsurfaces in acost-effective manner, using a variety of materials capable ofsatisfying application-specific requirements. Furthermore, thestructures can be casted directly on the surface to be coated, thussimplifying the installation process.

FIG. 2 illustrates graphs 22, 24 depicting data indicative ofinstantaneous normalized velocity u/U_(∞) for respective smooth andcoated cases, and graphs 26 and 28 depicting data indicative of the meanvertical velocity

V

/U_(∞), for the smooth and coated cases, respectively, in accordancewith an example embodiment. Graphs 22 and 24 demonstrate that the smoothcase has significantly more reverse flow, which is associated withseparated flow. In addition, graphs 26 and 28 demonstrate the area offlow moving away from the wall (upward velocity), which is linked toseparation.

The data contained in the various graphs shown herein (e.g., FIGS. 2, 3,4) is based on measurements that were performed in arefractive-index—matching (RIM) facility at the University of Illinoisat Urbana—Champaign with a diverging cross-section (e.g., see image 16in FIG. 1) at Re_(θ)≈1,200. As discussed previously, such measurementsor parameters are not to be considered limiting features of thedisclosed embodiments, but are provided herein for exemplary purposesonly.

The RIM allowed measurement of the velocity very near the wall, down toy⁺≈3.6 for the selected interrogation window. The flow field andturbulence statistics were compared with a smooth counterpart. Thecalculated uncertainty of the velocity measurement is 0.5% of U_(∞).Details of the experiments are described in the section “Materials andMethods” herein. The resulting velocity fields reveal significantdifferences between the flows over the smooth and coated walls.

Instantaneous velocity contours with superimposed mean streamlines(i.e., see graphs 22 and 24 in FIG. 2) illustrate a large region withreverse flow in the smooth case. In contrast, the divergent pillarsinduce a smaller separation bubble. Further, the reverse flow (blue)region is considerably smaller in the coated case.

FIG. 3 illustrates a graph 32 depicting superimposed contour lines forthe normalized mean streamwise velocity <U>/U_(∞) and graphs 34 and 36with data indicative of velocity profiles, in accordance with an exampleembodiment. In graph 32, solid lines represent “smooth” and dashed linesrepresent “coated”. The smooth case shown an approximately 60% largerarea with negative flow (black level). Graphs 34 and 36 respectivelyshow velocity profiles for <U>/U_(∞) and <V>/U_(∞), respectively, smoothand coated. Note that in graph 34, the inset 37 shows the region nearthe wall for <U>/U_(∞), where a larger negative portion in the smoothcase can be observed. Error bars represent SE (=u_(rms)√{square rootover (N)}, where N is the number of samples). For U, the error bars (notshown) are smaller than the symbol site).

The reduced flow separation is confirmed by the mean streamwise velocitycontours, which are shown superimposed for both cases (see graph 32 inFIG. 3A). The contours for the smooth case (solid lines) recover fartheraway from the wall, and the reverse flow (black contour) is considerablylarger over the smooth surface. The area with reverse flow is reduced byapproximately 60% in the presence of the microscale coating. Our dataalso reveal a downstream shift in the separation point of ˜0.46δ₀, whereδ₀ is the boundary layer thickness at the inlet of the expansion. Theeffect of the coating is also observed in the mean vertical velocityfield. When the flow is attached, this velocity component should remainnegative in this particular configuration. However, as observed in somecases, a higher upward velocity occurs in the smooth case, which ischaracteristic evidence that the boundary layer has detached from thewall (i.e., it is separated).

Despite lift and drag measurements not being performed for thisparticular study, previous wind-tunnel experiments carried out on acoated S809 airfoil have shown a 25-40% increase in the lift coefficientat angles between 8° and 16°. These results provide complementaryevidence of the functionality of pillars (such as shown, for example, inthe images 14 and 16) in reducing flow separation. This apparentfunctionality (lift coefficient increase) in wind-tunnel experimentsimplies that the coating also works in air. This supports the hypothesisthat the mechanism by which the surface coating reduces flow separationdoes not rely on hydrophobicity.

The differences between the two cases are highlighted in the selectedmean velocity profiles at x/δ₀=18.5 (see graphs 34 and 36 in FIG. 3).This is consistent with reduced blockage from a smaller recirculationbubble. The streamwise velocity in the coated case is higher near thewall (approximately 10% of the local average) than in the baseline. Theeffect of the coating is most noticeable from the wall up to y/δ≈0.6.The inset 37 in graph 34 of FIG. 3 shows a closer view near the wall,where the area with negative velocity, i.e., below the dashed line, islarger over the smooth surface. The difference larger, reaching almost50% increase in the coated case around y/δ≈0.3. It is also worth notingthat the vertical velocity does not recover completely at the edge ofthe boundary layer. This effect is due to the separation bubblepreventing the flow from moving downward along the wall.

When adding texture to a wall, there is a risk of increasing theproduction of turbulent kinetic energy, which is related to viscouslosses. The data discussed herein demonstrates differences in the TKEproduction between the two cases that are within the measurementuncertainty, suggesting that the pillars have minor effect on theturbulence production. This result is expected for “hydrodynamicallysmooth” walls.

While the results from the APG experiments show that the separationbubble is reduced and displaced downstream, the physical mechanismresponsible for these phenomena is not evident from the data. To shedlight on this mechanism, additional high-resolution experiments werecarried out over a flat plate coated with the same engineered divergingpillars at Re_(θ)≈3,600 (see details in the “Materials and Methods”section herein). For these measurements, the interrogation window wasplaced as close as y⁺≈1. This setup was chosen to avoid the unsteadinessof the separation bubble in the APG flow. It should be noted that giventhe thickness of the laser sheet (e.g., approximately 1 mm), weinherently probe the flow over several rows of pillars, which creates anaveraging effect in the transverse direction.

FIG. 4 illustrates graphs 42 and 44 depicting profile data and aschematic diagram 51 depicting the physical mechanism by which a groupof micropillars 48, 50, 52 modify the flow in the area near the flow, inaccordance with an example embodiment. Graph 42 shown in FIG. 4 plotsdata indicative of a wall-normal profile over someth and coated platesat x=2,100 mm. The coated case demonstrates a negative velocity in thevicinity of the wall, which is a result of suction between pillars(e.g., such as between micropillars 48, 50, and/or 52). Graph 44 depictsdata indicative of wall-normal Reynolds stress. The velocity fluctuationshows a marked increase in the area adjacent to the pillar canopy edge,which suggests that oscillations are induced by the pillars in the flowin the interface of the pillary canopy.

The schematic diagram 51 illustrates the physical mechanism by which themicropillars modify the flow in the area near the flow. Note that in theschematic diagram 51, flow is indicated by the arrow 46. That is, areasof low and high pressure create high- and low-velocity areas,respectively. They also create ejection and suction events asrepresented by the thick black arrows 53 and 55 shown in FIG. 4, whichincrease the wall-normal velocity fluctuations. The schematic diagram 51also demonstrates three distinct regions that arise in the flow: aninertia-dominated region, a viscous-dominated region, and an interfaceregion between these two layers.

The vertical velocity profile (see graph 42 in FIG. 4) for the coatedcase shows a downward (negative) flow near the wall. The inventorsbelieve that this downward flow may be due to a misalignment between thepillar rows and the bulk flow, creating a localized spanwise flow. Themechanism by which the pillars reduce flow separation can be gleanedfrom graph 44 in FIG. 4. The pillars generate oscillations in the innerlayer, which are reflected as a large peak in the wall-normal componentof the Reynolds stresses near the edge of the pillar canopy.Complementary insight is illustrated in the schematic diagram 51 of FIG.4. The pillars reduce the crosssectional area, accelerating the fluidpassing between them along the streamwise direction (red area). Thisacceleration decreases the pressure and generates suction. Additionally,pillars 48, 50 and/or 52 create a stagnation point by blocking some ofthe fluid. This increases the pressure and pushes fluid up, inducingfluid ejection.

Instead of the typical nonslip condition in canonical smooth walls, atthe top of the pillars (y=k), the fluid velocity is not zero between thepillars. Instead, an “interlayer” is created above the pillars (seeschematic diagram 51). In this layer a connection exists between theboundary layer (flow above the pillars 48, 50, 52) and the inner flow(i.e., within the canopy). Recalling the boundary layer momentumequation in the wall-normal direction,

$\begin{matrix}{{{\frac{1}{\rho}\frac{\partial{\langle P\rangle}}{\partial y}} = {\frac{\partial{\langle v^{2}\rangle}}{\partial y} + \frac{\partial{\langle v^{''2}\rangle}}{\partial y}}},} & \lbrack 1\rbrack\end{matrix}$

it is clear that

v²

and

P

are directly related; here

•

represents the time-averaging operator and

v^(″2)

is a dispersive stress arising from the spatial averaging in the x(streamwise) and z (spanwise) directions. Integrating Eq. 1 from the topof the diverging pillars to a point y above the surface, it follows that

(

P _(oi)

−

P

)/ρ=

v ²

−

v _(oi) ²

+

v ^(″2)

−

v _(oi) ^(″2)

,  [2]

where

P_(oi)

is the static pressure at the edge of the canopy; that is, y_(oi)=k=85μm Note that for the case of the smooth surface

v_(oi) ²

=0, but in the coated case

v_(oi) ²

≠0, as seen in the lower portion of graph 44 in FIG. 4.

The flow regime is significantly different within the micropillar layer,however. It has a Re_(k) less than or approximately equal to 1, based onthe geometry and the estimated friction velocity; thus, it is viscousdominated and governed by pressure gradient, i.e., Stokes flow. Equation1 can be used accordingly, recognizing that the gradient of thewall-normal Reynolds stress approaches zero. Therefore,

P_(ω)

≈

P_(oi)

within the pillar canopy, and the changes in the wall-normal Reynoldsstress are proportional to the pressure difference between the staticpressure at the wall, (P_(ω)), and the local pressure across theboundary layer. Consequently, it follows that

v _(oi) ²

=

v ²

+

v ^(″2)

−

v _(oi) ^(″2)

−(

P _(ω)

−

P

)/τ  [3]

This relation implies that the changes observed in the inner region for(v²) are likely due to suction and blowing events between the divergingpillars and along the high-momentum flow region. Despite the fact thatthese changes exist mainly below the buffer layer, significantvariations are observed in the outer layer, where the bubble resides.Consequently, this microscale surface passively modulates the smallscales of the flow in the wall region, which in turn affects the largescales in the outer flow. Given the size of the pillars, this result issurprising, but is consistent with observed findings of the propagationof the pressure perturbation over 35 times the pillar height.

The pressure modulation generated by the pillars can be described assmall-scale weak jetting events that may reenergize the boundary layerand delay separation; however, the pillars passively induce small-scaleperturbations over the entire surface. In the case of the divergentpillars, the contraction in the cross-sectional area is greater,amplifying the flow acceleration between the pillars. The regions ofejections and suctions are increased in the viscous sublayer. For thesmooth case, this increase occurs in the buffer layer, suggestingevidence of an interlayer above the pillar, which is consistent withEquation 3.

The combined results from such experiments indicate that it is throughpressure changes at the interlayer, between viscous-dominated flowwithin the canopy and the inertia-dominated flow above the pillars, thatthe large scales of the flow are affected. Thus, the wall normalReynolds stress at the interface,

v²

, modulates the flow between the diverging pillars (suction and blowing)by interacting with the pressure difference,

P_(ω)

−

(P)

, across the roughness interlayer. It must be stressed that the diameterof the pillar is the largest at the interlayer between the roughnesscanopy and the boundary layer, and therefore its effect is largestprecisely in this region of the flow.

The pillars 48, 50 and 50 shown in the schematic diagram 51 in FIG. 4are thus examples of a type of bio-inspired fibrillar structure. Theyhave the demonstrated the ability to reduce the drag by more than 10%.The disclosed embodiments are based on studies of the effects of suchfibrillar structures on flow separation. The inventors have discoveredthat the micro-scale fibrillar coating significantly reduced flowseparation by reducing the size of the separation bubble and pushing theseparation point further downstream. The inventors have accomplishedthis without increasing the turbulent kinetic energy (which isby-product of texturizing a surface). These results starkly oppose thenotion that rough surfaces facilitate flow separation. The configurationand makeup of the surface coating in the disclosed embodimentsdemonstrate how and why the surface coating is so effective in reducingthe separation bubble and displacing the separation bubble downstream.

Flow separation on moving bodies has a negative effect on energyefficiency. Reducing recirculating regions is a key in the design ofenergy-efficient systems. Efficient design decreases fuel consumptionand pollutant emissions, including the systems' carbon footprint. Theengineered bio-inspired coating presented herein aims to contribute inthat direction. The relative ease of manufacturing and installation andits cost effectiveness, as well as its functionality under both wet anddry conditions, make it a versatile solution of potentially high impactin a broad range of applications, including transportation, wind power,and underwater vehicles.

Conclusions and Outlook

We have tested the flow control properties of an engineered bio-inspiredsurface coating. Our results confirm the functionality of the coating,which mitigated flow separation without a noticeable increase in theproduction of the turbulent kinetic energy. The microscale surfacecoating shifts the separation point downstream and significantly reducesthe area of negative flow. The coating can be manufactured and installedwith relative ease and is cost-effective in comparison with othersolutions manufactured using 3D printing. The physical mechanism bywhich the coating works does not rely on (super)hydrophobicity. Instead,it relies on the generation of distributed wall-normal perturbations,giving it the versatility to work in liquid and gas media. These resultshave important implications in flow control, with applications in bothpower generation, e.g., wind turbines, and energy-efficient transportvehicles. These capabilities considerably increase the potential impactof the engineered coating.

While our results demonstrate the functionality and describe the workingmechanism of the micropillars, it is necessary to test the surfacecoating under other flow conditions and different geometricconfigurations, e.g., spacing and height. Adapting the micropillarcoating to a diverse array of applications will maximize the impact ofthis engineered surface on energy and transport systems.

Materials and Methods

FIG. 5 illustrates a schematic diagram 60 of the APG test section of awind-turbine, in accordance with an example embodiment. In theexperiments associated with the schematic diagram 60, the boundary layerdevelops in an approach channel of height H=45 mm and a length L=1,250mm. The origin of the coordinate system (x=0, y=0) is set at the bottomwall of the channel at the beginning of the expansion. The micropillarcoating (shaded area) was applied from x=−50 mm, and the X835 section is370 mm long.

FIG. 6 illustrates a schematic diagram 80 depicting a ZPG test sectionand FIG. 6A illustrates an inset thereof, in accordance with an exampleembodiment. The boundary layer develops over a smooth region of 1,650 mmfollowed by a coated plate of 550 mm length (R_(θ)3,600), using the samediverging pillar geometry (e.g., shape, size, and spacing) as in the APGexperiments. Careful alignment of the plates was performed by using20-μm shims. In FIG. 6, example pillars 84 and 86 are shown in the inset82 in FIG. 6A.

The experiments were performed in a RIM flume of a 112.5×112.5 mm² testsection at the University of Illinois (laboratory of L.P.C.). Theworking fluid was a sodium iodide solution (63% by weight) with akinematic viscosity v=1.1×10⁻⁶ m²/s and a density ρ=1,800 kg/m³. Theminimum reflection from the wall allowed measurements within the viscoussublayer (y⁺≈3.6). The facility was adapted with a diverging wall (seeFIG. 5) to induce adverse pressure gradient and flow separation. Theexperiments were performed at a Reynolds number Re_(H)=U₀H_(1/2)/v=4,600(or in terms of the momentum thickness, Re_(θ)≈560) measured rightupstream of the expansion (x=0), where U_(o)=0.225 m/s is the centerlinevelocity and H_(1/2)=H/2. The boundary layer thickness at the inletδ_(o)=16:2 mm, and the normalized roughness height k⁺≅1 is estimatedwith c_(f)=0.026/Re_(x) ^(1/7). The inlet velocity profile for bothcases differed by less than or equal to 1%. In the FOV (Field of View)shown in FIG. 2, for example, δ≈27.5 mm and Re_(θ)≈1,200.

Flat-plate [zero pressure gradient (ZPG)], high-resolution experimentswere carried out in the RIM flume described above to assess the changesin the velocity field near the wall. For this set of experiments, thecross-section (112.5 mm×112.5 mm) was unobstructed. As illustrated inFIG. 6, the bottom wall was coated over a 550-mm span past a 1,650-mmsmooth development region. The height of the coated plate was adjustedto minimize disturbances. Furthermore, to reduce misalignment effects,the flow was probed 500 mm into the coated section. The mean free streamvelocity U_(∞)=0.8 m/s, equivalent to a momentum-based Reynolds numberRe_(θ)=3,600. For these experiments, the field of view was considerablysmaller than in the APG experiments, allowing us to resolve the viscoussublayer, down to a y⁺≈1.

Regarding particle image velocimetry, planar (two-dimension,two-component) particle image velocimetry (PIV) was used to measure thevelocity field in a vertical plane at the axis of the diverging flume.An 11-MP camera (e.g., 2,700×4,000 pixels²) and a pulsed, dual-headNd:YAG laser were used for image capture. The APG experiments had aresolution of 46 μm/pixel, resulting in a field of view of approximately182×123 mm². Each experimental run involved 4,000 PIV realizations. Thedata processing was performed with a final interrogation window of 16×16pixels² with 50% overlap, resulting in a vector separation Δx=Δy=365 μm.

The ZPG experiments used the same imaging system described above, butwith higher resolution and a different processing algorithm. The opticalfield of view for these experiments was 26 mm×17.4 mm. A PIV plus PTV(particle tracking velocimetry) processing (LaVision) was used to obtainthe velocity field. The algorithm performed two PIV passes, 32×32 pixelsand 16×16 pixels, with a final PTV pass. The mean velocity field wascalculated from 2,000 samples with a vector separation of 6.5 μm.

FIG. 7 illustrates a flow chart of operations depicting a method 100 forfiber fabrication in accordance with an example embodiment. The method100 shown in FIG. 7 can be utilized to configure the disclosed divergingpillar array described herein, which is composed of a group of uniformlydistributed cylindrical micropillars. Fiber fabrication (e.g.,fabrication of a group of fibrillar structures) can involve thefabrication of the disclosed microscale coating using a method composedof photolithography, micromolding, and diptransfer printing.

As shown at block 102, a step or operation can be implemented in which amaster template of cylindrical fibers is first fabricated usingphotolithography from photoresist (e.g., SU-8 2100; MicroChem). Next, asshown at block 104, a step or operation can be implemented in which ashape-complementary mold, which features the negative of cylindricalfibers, is manufactured by casting the cylindrical master with siliconerubber (e.g., Mold Max 27T; Smooth-On). Then, as depicted at block 106,a step or operation can be implemented in which the complementary moldis then cast with polyurethane (e.g., ST 3180; BJB Enterprises) tomanufacture cylindrical fibers, which are an exact replica of the masterfibers.

The second step of the fabrication forms the divergent tip, a featuresimilar to the shark denticle. As indicated at block 108, a step oroperation can be implemented in which the polyurethane cylindricalfibers are placed onto a very thin film of liquid polyurethane, formedby spin coating the liquid polyurethane on a polystyrene substrate,using a spinner (e.g., WS-650 MS; Laurell Technologies). Next, asdepicted at block 110, a step or operation can be implemented to removethe cylindrical fibers from the thin liquid film. Note that when thecylindrical fibers are removed from the thin liquid film, they retainsome of the liquid polymer on the tip of each individual fiber.

Immediately after this step, as shown at block 112, a step or operationcan be implemented in which the fiber array is placed onto alow-surface-energy dipping surface, a polypropylene substrate, allowingthe liquid polymer to spread and morph into the desired shape.Thereafter, as illustrated at block 114, a step or operation can beimplemented in which the pillars with divergent tips are obtained byremoving the fibers from the dipping surface after the liquid polymer onthe tips of the fibers cures. This step creates the master template forthe fiber array, the result of which is indicated by block 116. As shownnext at block 118, a step or operation can be implemented in which acomplementary mold is fabricated by casting the fibers with siliconerubber. Then, as described at block 120, a step or operation isimplemented, which this mold is cast with a rigid polyurethane (e.g.,Crystal Clear 200; Smooth-On) on an acrylic backing to obtain divergingpillar arrays such as those utilized in the disclosed experimentalembodiments.

It is understood that the specific order or hierarchy of steps,operations, or instructions in method 100 is an illustration of anexemplary process. Based upon design preferences, it is understood thatthe specific order or hierarchy of such steps, operation or instructionsin such a process as discussed and illustrated herein may be rearranged.The accompanying claims, for example, present elements of various steps,operations or instructions in a sample order, and are not meant to belimited to the specific order or hierarchy presented.

Flow separation and vortex shedding are some of the most commonphenomena experienced by bluff bodies under relative motion with thesurrounding medium. They often result in a recirculation bubble inregions with adverse pressure gradient, which typically reducesefficiency in vehicles and increases loading on structures. As discussedherein, the ability of an engineered coating to manipulate thelarge-scale recirculation region was tested in a separated flow atmoderate momentum thickness Reynolds number, Re_(θ)=1,200. The disclosedembodiments demonstrate that the coating, composed of uniformlydistributed cylindrical pillars with diverging tips, successfullyreduces the size of, and shifts downstream, the separation bubble.Despite the so-called roughness parameter, k⁺≈1, falling within thehydrodynamic smooth regime, the coating is able to modulate thelarge-scale recirculating motion. Remarkably, this modulation does notinduce noticeable changes in the near-wall turbulence levels. Supportedwith experimental data and theoretical arguments based on the averagedequations of motion, the inventors suggest that the inherent mechanismresponsible for the bubble modulation is essentially unsteady suctionand blowing controlled by the increasing cross-section of the tips. Thecoating can be easily fabricated and installed and works under dry andwet conditions, increasing its potential impact on a diverse range ofapplications.

It should be appreciated that the disclosed coating offers a number ofadvantages. For example, in addition to facilitating a reducing in noiseand vibrations due to the disclosed reduction in the size of theseparation bubble, such a coating also facilitates a reduction in drag(i.e., recall that the coating can be implemented in dry or wetconditions). One particular area where the disclosed coating offers anadvantage is the field of biofouling. Biofouling or biological foulinginvolves the accumulation of microorganisms, plants, algae, or animalson wetted surfaces. Such accumulation is referred to as epibiosis whenthe host surface is another organism and the relationship is notparasitic.

Antifouling is the ability of specifically designed materials andcoatings such as the coating described herein to remove or preventbiofouling by any number of organisms on wetted surfaces. Sincebiofouling can occur almost anywhere water is present, biofouling posesrisks to a wide variety of objects such as medical devices andmembranes, as well as to entire industries, such as paper manufacturing,food processing, underwater construction, and desalination plants. Thus,the disclosed coating can comprise in some alternative exampleembodiments, an antifouling coating or material.

Based on the foregoing, it can be appreciated that a number of preferredand alternative example embodiments are disclosed herein. For example,in one embodiment a coating apparatus or device can be configured whichincludes a coating composed of a plurality of fibrillar structures,wherein each fibrillar structure among the plurality of fibrillarstructures is configured with a diverging tip so that the coatingreduces a size of and shifts downstream, a separation bubble, andmodulates large-scale recirculating motion. The coating can facilitate areduction in noise and vibrations due to the reduction in the size ofthe separation bubble. The coating also facilitates a reduction in drag.In an example embodiment, the coating can be configured as anantifouling coating.

Each fibrillar structure among the plurality of fibrillar structurescomprises a cylindrical micropillar and the plurality of fibrillarstructures comprises a plurality of uniformly distributed cylindricalmicropillars. In addition, the coating can be configured to functionunder a dry condition or a wet condition. Additionally, the coating isconfigured to mitigate flow separation without a noticeable increase ina production of turbulent kinetic energy.

The coating also can be configured in some example embodiments toinclude a microsurface coating that shifts the separation pointdownstream and reduces the area of negative flow. In addition, thecoating can be configured to rely on the generation of distributedwall-normal perturbations. In another example embodiment, the coatingcan include a micropillar coating composed of the aforementionedplurality of fibrillar structures.

It will be appreciated that variations of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. It will alsobe appreciated that various presently unforeseen or unanticipatedalternatives, modifications, variations or improvements therein may besubsequently made by those skilled in the art, which are also intendedto be encompassed by the following claims.

What is claimed is:
 1. A coating apparatus, comprising a coatingcomprising a plurality of fibrillar structures, wherein each fibrillarstructure among said plurality of fibrillar structures is configuredwith a diverging tip so that said coating reduces a size of and shiftsdownstream, a separation bubble, and modulates large-scale recirculatingmotion.
 2. The apparatus of claim 1 wherein said coating facilitates areduction in noise and vibrations due to said reduction in said size ofsaid separation bubble.
 3. The apparatus of claim 1 wherein said coatingfacilitates a reduction in drag.
 4. The apparatus of claim 1 whereinsaid coating comprises an antifouling coating.
 5. The apparatus of claim1 wherein each fibrillar structure among said plurality of fibrillarstructures comprises a cylindrical micropillar and said plurality offibrillar structures comprises a plurality of uniformly distributedcylindrical micropillars.
 6. The apparatus of claim 1 wherein saidcoating is configured to function under a dry condition.
 7. Theapparatus of claim 1 wherein said coating is configured to functionunder a wet condition.
 8. The apparatus of claim 1 wherein said coatingmitigates flow separation without a noticeable increase in a productionof turbulent kinetic energy.
 9. The apparatus of claim 1 wherein saidcoating comprises a microsurface coating that shifts a separation pointdownstream and reduces an area of negative flow.
 10. The apparatus ofclaim 1 wherein said coating relies on a generation of distributedwall-normal perturbations.
 11. The apparatus of claim 1 wherein saidcoating comprises a micropillar coating comprising said plurality offibrillar structures.
 12. A coating apparatus, comprising a coating thatfacilitates a reduction in noise and vibrations, said coating comprisinga plurality of fibrillar structures, wherein each fibrillar structureamong said plurality of fibrillar stuctures is configured with adiverging tip so that said coating reduces a size of and shiftsdownstream, a separation bubble, and modulates large-scale recirculatingmotion and wherein said each fibrillar structure among said plurality offibrillar structures comprises a cylindrical micropillar, said pluralityof fibrillar structures comprising a plurality of uniformly distributedcylindrical micropillars and wherein said coating facilitates saidreduction of said noise and vibrations due to said reduction in saidsize of said separation bubble.
 13. The apparatus of claim 12 whereinsaid coating further facilitates a reduction in drag.
 14. The apparatusof claim 12 wherein said coating further facilitates a prevention of ora reduction in biofouling.
 15. The apparatus of claim 12 wherein saidcoating is configured to function under either wet or dry conditions.16. The apparatus of claim 12 wherein said coating comprises abio-inspired surface coating.
 17. The apparatus of claim 12 wherein saidcoating mitigates flow separation without a noticeable increase in aproduction of turbulent kinetic energy.
 18. The apparatus of claim 12wherein said coating comprises a microsurface coating that shifts aseparation point downstream and reduces an area of negative flow. 19.The apparatus of claim 12 wherein said coating relies on a generation ofdistributed wall-normal perturbations.
 20. A method of configuring acoating apparatus, said method comprising: providing a coatingcomprising a plurality of fibrillar structures; configuring eachfibrillar structure among said plurality of fibrillar stuctures with adiverging tip so that said coating reduces a size of and shiftsdownstream, a separation bubble, and modulates large-scale recirculatingmotion, wherein said coating facilitates a reduction in noise andvibrations due to said reduction in said size of said separation bubble,and further facilitates a reduction in drag.